Titlebook: Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I; Dirichlet Boundary C Jérôme Le Rousseau,Gilles

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https://doi.org/10.1007/978-94-011-5428-4an estimates has gone beyond the original domain; they are also used in the study of stabilization and controllability properties of partial differential equations, two applications we shall consider in this book. Inverse problems are also a field of applications for Carleman estimate; we shall however not touch upon that subject.

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Atanu Biswas,Jean-Francois Angers, in the time interval (0, .), with homogeneous Dirichlet boundary conditions, and for an initial condition .. in ..(.), is given by . The function . is the control. The goal is to drive the solution . to a prescribe state at time . > 0, yet only acting in the sub-domain .. We shall make precise what can actually be achieved below.

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1421-1750 inequality.  The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet d978-3-030-88676-9978-3-030-88674-5Series ISSN 1421-1750 Series E-ISSN 2374-0280

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(Pseudo-)Differential Operators with a Large Parameter

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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume IDirichlet Boundary C

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Introductionons. Estimates of this type now bear his name. In the late 50s A.-P. Calderón and L. Hörmander further developed Carleman’s method. To this day, the method based on Carleman estimates remains essential to prove unique continuation properties. In more recent years, the field of applications of Carlem

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Stabilization of the Wave Equation with an Inner Dampingsay, homogeneous Dirichlet boundary conditions. Here .(.) is a nonnegative bounded function. In the case . ≡ 0 the solution exists for . with an energy that remains constant with respect to .. We shall prove here that if . > 0 on a nonempty open subset . then the energy decays to . as . → +.. The te